The generally accepted methods for time series forecasting are: extrapolation of linear regression, extrapolation of polynomial regression, autoregressive moving average (ARMA), and exponential smoothing as discussed by Diggle, Time Series: A Biostatistical Introduction, Oxford University Press, Oxford, (1990). Linear regression models are an acceptable means of forecasting, provided that the data being analyzed are linear. In the case where the data in question are nonlinear, polynomial regression is often used to model the data.
Autoregressive (ARMA) methods have been used with success in forecasting where the underlying phenomena are stationary (or can be converted to stationary), with superimposed fluctuations expressible as random white noise. These two requirements can be met for some physiologic variables, but plasma glucose levels in diabetic patients generally do not fit these requirements. The method of exponential smoothing is a special case of the ARMA method. The above methods forecast the future value of a variable based on the value of that variable at previous time points. Information on the first and second derivative of the variable with respect to time is not included. Inclusion of these time derivatives can substantially increase the accuracy of the forecasting method in the situation where the future value of a variable depends on its time rate of change.